Question

lines (ell) and (m) are intersected by transversal (t) and (ellparallel m).
if (mangle2 = 112), what is (mangle7)?
(mangle7=)

Explanation:

Step1: Find the measure of ∠4

Since ∠2 and ∠4 are vertical angles, vertical angles are equal.
So, \(m\angle4 = m\angle2=112^{\circ}\)

Step2: Use the property of parallel lines

Because \(\ell\parallel m\), ∠4 and ∠6 are alternate - interior angles. Alternate - interior angles are equal. So, \(m\angle6 = m\angle4 = 112^{\circ}\)

Step3: Find the measure of ∠7

Since ∠6 and ∠7 are supplementary angles (they form a linear pair), \(m\angle6+m\angle7 = 180^{\circ}\)
Substitute \(m\angle6 = 112^{\circ}\) into the equation: \(112^{\circ}+m\angle7=180^{\circ}\)
Then \(m\angle7=180^{\circ}- 112^{\circ}=68^{\circ}\)

Answer:

\(68\)